Alcaraz has enjoyed a hugely impressive season to date, having last week added the Barcelona Open to the titles won in Rio de Janeiro and Miami already in 2022.
After that triumph in Catalonia, Alcaraz, who turns 19 next week, became the youngest male player to break into the top 10 since Nadal 17 years ago.
He boasts a record of 23-3 this year, one of those defeats coming at the hands of Spanish great Nadal in the semi-finals of Indian Wells in March.
That encounter lasted over three hours, with Nadal digging deep in California to prevail 6-4 4-6 6-3, only to lose in the final to Taylor Fritz.
Nadal was clearly troubled by injury during his defeat to Fritz and has subsequently taken a break to recover from a rib problem.
The pair is set to collide once again in Madrid next week should both players come through their second and third-round matches.
Speaking ahead of the draw, Alcaraz revealed he has taken inspiration from facing Nadal, who won a record 21st Majors after triumphing at the 2022 Australian Open in January.
"I learned about the fighting spirit, of never giving up," the teenager said on Spanish talk show El Hormiguero.
"Many people will have also seen the Australian Open match, he was losing and came back almost miraculously.
"From that match against him [at Indian Wells] I get the fighting spirit, never give up and fight until the last ball."
No.1 seed Novak Djokovic is also in Alcaraz and Nadal's side of the Madrid Open draw, while Andy Murray and Dominic Thiem will meet in the pick of the first-round clashes.
